Abstract
It is proved that the free energy of a system ofn-dimensional spins with Kac type potential is equal, in the infinite range zero strength limit, to the free energy of the corresponding Curie-Weiss system in which every spin interacts equally with every other spin.
Similar content being viewed by others
References
Lebowitz, J. L., Penrose, O.: J. Math. Phys.7, 98 (1966)
Thompson, C. J.: Mathematical statistical mechanics, Appendix C. Macmillan N.Y. 1972.
Stanley, H. E.: Phys. Rev. Lett.20, 589 (1968)
Stanley, H. E.: Phys. Rev.176, 718 (1968)
Kac, M., Thompson, C. J.: Physica Norvegica5, 163 (1971)
Silver, H., Frankel, N. E., Ninham, B. W.: J. Math. Phys.13, 468 (1972)
Cramer, H.: Mathematical methods in statistics, p. 118. Princeton University Press 1951.
Grenander, U., Szegö, G.: Toeplitz forms and their applications. Berkeley, California: University of California Press 1958.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thompson, C.J., Silver, H. The classical limit ofn-vector spin models. Commun.Math. Phys. 33, 53–60 (1973). https://doi.org/10.1007/BF01645606
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645606